Two sample t test - equal variances assumed - overview

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Within each population, the scores on the dependent variable are normally distributed

The standard deviation of the scores on the dependent variable is the same in both populations: $\sigma_1 = \sigma_2$

Group 1 sample is a simple random sample (SRS) from population 1, group 2 sample is an independent SRS from population 2. That is, within and between groups, observations are independent of one another

Test statistic

$t = \dfrac{(\bar{y}_1 - \bar{y}_2) - 0}{s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}} = \dfrac{\bar{y}_1 - \bar{y}_2}{s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}}$
$\bar{y}_1$ is the sample mean in group 1, $\bar{y}_2$ is the sample mean in group 2,
$s_p$ is the pooled standard deviation,
$n_1$ is the sample size of group 1, $n_2$ is the sample size of group 2. The 0 represents the difference in population means according to the null hypothesis.

Cohen's $d$:
Standardized difference between the mean in group $1$ and in group $2$:
$$d = \frac{\bar{y}_1 - \bar{y}_2}{s_p}$$
Indicates how many standard deviations $s_p$ the two sample means are removed from each other